A lotta MathJax

MathJax V3
1

OK, here’s a topic with a lot of typeset math. The topic consists of

  • An initial post with
    • 50 LaTeX math expressions,
    • 149 inline math expressions, and
    • 84 Ascii Math expressions

There are also 3 long responses.

  1. Lorem ipsum dolor sit amet x^2 + 1 , consectetur a/b adipiscing elit. Sed \alpha + \beta interdum x^2 + y^2 = 1 nec \sqrt{n} vitae nisl.
\int_0^1 e^{-x^2} \, dx
  1. Phasellus quis a_n urna x/(y+1) sit amet k^2 - 4m turpis sum_{i=1}^n i dapibus.
\begin{aligned} f(x) &= x^2 + 3x - 2 \\ &= (x+1)(x+2) \end{aligned}
  1. Suspendisse vel \theta/2 massa sqrt(3)/2 eget x_i turpis n! varius a=b .
\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
  1. Aenean vitae x^3 urna y' = 3y feugiat \pi r^2 sed d/dx(x^n) in x=y .
\sum_{n=0}^\infty \frac{x^n}{n!}
  1. Mauris at \mu + \sigma odio tan(pi/4)=1 vel x_0 sem u+v rutrum a*(b+c) .
\iint_D (x^2 + y^2)\, dA
  1. Curabitur a/b + c/d non Q(x) dui x+y sed f'(x) magna x^2 - y^2 .
\prod_{k=1}^n (1 + a_k)
  1. Quisque interdum r(t) elit sin(pi/6) vitae 2^n dictum \log x et m/n .
\begin{aligned} y' &= 3y - 2x \\ y'' &= 9y - 2 \end{aligned}
  1. Donec ut cuberoot(2) metus \phi quis x_1 + x_2 purus |x| eget x=y/z arcu.
\oint_C (x\,dy - y\,dx)
  1. Integer feugiat x*(y+z) sapien 1/n et a^3 orci sqrt(5) ac \nabla f .
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}
  1. Sed sit amet \beta_0 lacus ln(2) id z^k non x^{-1} lorem a=b/c .
\int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}
  1. Nulla facilisi x=y sed f(x)=0 nisl 3^k placerat n^2 - 1 eget x^2+xy+y^2 .
\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}
  1. Duis in y=ax+b nibh a/(b+c) ac r^2 sapien sum(i^2) volutpat x_3 .
\begin{aligned} A &= \begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix} \\ A^2 &= A \cdot A \end{aligned}
  1. Praesent eget x=(y+z) sem \delta ac n^k quis uv est a->b .
\frac{d}{dx}(x^x) = x^x(\ln x + 1)
  1. Suspendisse s_n ac x+y=z eros p/q nec 1/(x+1) dui sqrt(7) .
\lim_{x\to 0} \frac{\sin x}{x} = 1
  1. Vivamus congue \gamma dui x^y et x_4 sem x^{-2} vitae c+d .
\begin{bmatrix} 1 & 2 & 1 \\ 0 & 1 & 3 \\ 2 & 0 & 1 \end{bmatrix}
  1. Vestibulum \omega t eget a/(b-c) nibh x_5 quis k! turpis x/y+z .
\int_0^\infty x^n e^{-x}\, dx = n!
  1. Sed pretium sqrt(1-x^2) lorem \int_0^t at g(x) vitae uv+wx nisi a=b .
\begin{aligned} \nabla \cdot \mathbf{F} &= \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} + \frac{\partial F_z}{\partial z} \end{aligned}
  1. Cras non sin(x)/x urna x_6 vel 3n+1 quam r^3 eget a=b .
\sum_{k=0}^\infty (-1)^k x^{2k}
  1. Proin facilisis x=y-z dui m^2 ac w(t) sed t_0 augue sqrt(11) .
\int_0^1 x(1-x)\, dx
  1. Integer nec x^7 lorem x/y eget 2^{n+1} arcu \alpha\beta non a*b .
\begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix}
  1. Mauris f''(x) velit x=y eget p_n metus q+r mollis sqrt(13) .
\frac{1}{1-x} = \sum_{n=0}^\infty x^n
  1. Donec a a_{ij} enim x^(1/3) sed |y| felis n_0 id x-y .
\begin{aligned} x' &= Ax \\ x(0) &= x_0 \end{aligned}
  1. Fusce pretium x/y=z leo b_k ac p(x) at 4x vel x! .
\det \begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc
  1. Vivamus gravida cuberoot(7) magna r_n nec x-1 ut 2x+3 sum(i) .
\int e^{ax} \sin(bx)\, dx
  1. Sed at a=b/c massa q_n id g'(x) eget x^9 sem.
\begin{aligned} y &= C_1 e^{r_1 t} + C_2 e^{r_2 t} \\ r_{1,2} &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{aligned}
  1. Quisque f(x)=x^3 luctus tan(x) lorem j(t) eu i^2+1 a=b .
\oint_C \mathbf{F}\cdot d\mathbf{r}
  1. In non sqrt(2) arcu 2\pi r pretium 1/(1+x) eget a^n x+y .
\sum_{n=1}^\infty \frac{1}{n^2}
  1. Curabitur x/(x+1) varius \sigma^2 ac z_1 vitae u'=f(u) elit.
\begin{aligned} \frac{dx}{dt} &= x(1-x) \\ \frac{dy}{dt} &= -y \end{aligned}
  1. Pellentesque 3x-1 id x=y quam p(t) a q(t) sem.
\int_0^\infty \frac{\sin x}{x}\, dx = \frac{\pi}{2}
  1. Nunc pharetra sqrt(17) metus 3^{n+1} vel x=yz ac x+1 felis.
\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}
  1. Sed nec x/y=z nulla p_3 vel x^{10} ut r+s tellus.
\sum_{k=1}^\infty \frac{(-1)^k}{k}
  1. Donec non a/b orci \ln x sit t_1 amet x^5 elit.
\int_0^1 (x^3 + x^2)\, dx
  1. Aliquam sqrt(19) ut q/p tortor |x+1| viverra n-1 velit.
\begin{aligned} \nabla \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \partial_x & \partial_y & \partial_z \\ P & Q & R \end{vmatrix} \end{aligned}
  1. Mauris x^{1/2} sit a=b amet w_n non x^n mi z^3 .
\int \frac{1}{x^2+1}\, dx
  1. Etiam f'(x) at y=x risus 1/(x^2) quis 3x mauris sqrt(23) .
\sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}
  1. Aenean x=y vitae r_2 magna s^2 posuere x^{-3} 1/(1+x) .
\begin{bmatrix} 1 & 3 & 5 \\ 2 & 4 & 6 \end{bmatrix}
  1. Sed viverra x*y leo p_7 eget u_1 nisl sqrt(29) .
\frac{d}{dx}(\sin x) = \cos x
  1. Praesent a=b+c tincidunt x^8 id 2t+7 risus s_n .
\int_0^\pi \sin x\, dx = 2
  1. Curabitur 1/(x+2) auctor 2^k et u'=ku nec v+w massa.
\prod_{n=1}^N n = N!
  1. Donec x_{ij} posuere x=y nunc x! quis t^3+1 sem sqrt(31) .
\int (3x^2 - 2x)\, dx = x^3 - x^2 + C
  1. Pellentesque x/(y+1) non m(x) erat p/q feugiat e^t vel velit.
\sum_{n=0}^\infty \frac{x^n}{n!}
  1. Duis r_8 eget x^2 - 5 augue sqrt(37) pharetra uvw .
\det\begin{bmatrix} 3 & 1 & 4 \\ 1 & 5 & 9 \\ 2 & 6 & 5 \end{bmatrix}
  1. Morbi x*y/z luctus n^n id u^{-1} nec 3x+4 tortor.
\int_0^1 \ln x\, dx
  1. In eget x^(-1) ante t_n id x^3 - 1 sed \sqrt{x} erat.
y' + p(x)y = q(x)
  1. Integer x+y=z eu w(t) massa p^2 vitae r^4 dui a=b .
\oint_C \mathbf{E}\cdot d\mathbf{l}
  1. Aliquam x=y/z sodales x_8 sed 1/(2x) vel a^k nibh sqrt(41) .
\int (x^4 - x)\, dx
  1. Vestibulum x^{11} est a*(b+c) non 2^p aliquet z(w) .
\begin{bmatrix} 4 & 1 \\ 2 & -3 \end{bmatrix}
  1. Proin sqrt(43) magna x/y nec x+3 sed \phi^2 quam.
\sum_{n=1}^\infty \frac{1}{n}
  1. Vestibulum a=b eros t^5 id q(x) vitae r(x) arcu.
\int_0^1 x^x\, dx
  1. Phasellus x_{10} vitae x-y+z eros e^{i\theta} vel f_0 sed sqrt(47) .
\frac{d}{dt} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}
2
  1. Lorem ipsum dolor sit amet x^2 + 1 consectetur a/b adipiscing elit \alpha + \beta vitae x^2+y^2=1 orci.
\int_0^1 e^{-x^2}\, dx
  1. Sed sit amet \theta/2 massa sqrt(3)/2 porttitor x_i feugiat n! et a=b ligula.
\begin{bmatrix} 1 & \theta \\ \alpha & \beta \end{bmatrix}
  1. Integer id \pi r^2 sem x^3 sed y'=3y non d/dx(x^n) eget x=y .
\sum_{k=0}^\infty x^k
  1. Curabitur \mu+\sigma non tan(pi/4)=1 purus x_0 sit u+v amet a*(b+c) arcu.
\iint_D (x^2+y^2)\, dA
  1. Vivamus pharetra Q(x) augue a/b+c/d id x+y auctor x^2-y^2 nec f'(x) .
\prod_{k=1}^n (1+a_k)
  1. Proin nec r(t) lacus sin(pi/6) vitae 2^n at \log x dui m/n .
\begin{aligned} y' &= 3y-2x \\ y'' &= 9y-2 \end{aligned}
  1. Duis in \phi orci cuberoot(2) et x_1+x_2 magna |x| eget x=y/z .
\oint_C (x\,dy - y\,dx)
  1. In ac 1/n nunc x*(y+z) vel a^3 et sqrt(5) nibh \nabla f .
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}
  1. Etiam vel \beta_0 metus ln(2) nec z^k convallis x^{-1} vitae a=b/c .
\int_{-\infty}^{\infty} e^{-x^2}\, dx
  1. Mauris vel f(x)=0 sem x=y id 3^k suscipit n^2-1 porta x^2+xy+y^2 .
\sum_{k=1}^n k^2
  1. Fusce a y=ax+b libero a/(b+c) tincidunt r^2 urna sum(i^2) id x_3 .
A=\begin{bmatrix}2 & -1 \\ 1 & 3\end{bmatrix}
  1. Cras non \delta justo x=(y+z) ut n^k vehicula uv a->b .
\frac{d}{dx}(x^x)
  1. Suspendisse s_n at x+y=z elit p/q aliquet 1/(x+1) scelerisque sqrt(7) .
\lim_{x\to 0} \frac{\sin x}{x}
  1. Donec porttitor \gamma arcu x^y vel x_4 non x^{-2} eget c+d .
\begin{bmatrix} 1&2&1\\ 0&1&3\\ 2&0&1 \end{bmatrix}
  1. Pellentesque \omega t mi a/(b-c) id x_5 rutrum k! vitae x/y+z .
\int_0^\infty x^n e^{-x}\, dx
  1. Morbi vel \int_0^t arcu sqrt(1-x^2) eget g(x) at uv+wx diam a=b .
\nabla \cdot \mathbf{F}
  1. Quisque eget x_6 eros sin(x)/x vel 3n+1 tincidunt r^3 et a=b .
\sum_{k=0}^\infty (-1)^k x^{2k}
  1. Vestibulum m^2 eu x=y-z augue w(t) non t_0 at sqrt(11) orci.
\int_0^1 x(1-x)\, dx
  1. Aenean aliquam x^7 lorem x/y eget 2^{n+1} lectus \alpha\beta a*b .
\begin{bmatrix} 1&4&7\\ 2&5&8\\ 3&6&9 \end{bmatrix}
  1. Etiam vel f''(x) orci x=y nec p_n sed q+r purus sqrt(13) .
\frac{1}{1-x}
  1. Nam vitae a_{ij} lacus x^(1/3) sed |y| nisl n_0 x-y .
x'=Ax
  1. Proin eget b_k dui x/y=z ac p(x) non 4x nec x! .
\det\begin{bmatrix}a&b\\c&d\end{bmatrix}
  1. Integer placerat r_n orci cuberoot(7) eget x-1 eu 2x+3 at sum(i) .
\int e^{ax}\sin(bx)\, dx
  1. Sed tempus q_n velit a=b/c a g'(x) dapibus x^9 nec.
y=C_1e^{r_1t}+C_2e^{r_2t}
  1. Pellentesque f(x)=x^3 nisl tan(x) vitae j(t) ut i^2+1 a=b .
\oint_C \mathbf{F}\cdot d\mathbf{r}
  1. Cras sed 2\pi r lorem sqrt(2) id 1/(1+x) eget a^n x+y .
\sum_{n=1}^\infty \frac{1}{n^2}
  1. Phasellus vel \sigma^2 velit x/(x+1) quis z_1 et u'=f(u) arcu.
\frac{dx}{dt}=x(1-x)
  1. Duis at 3x-1 sem x=y aliquam p(t) eget q(t) velit.
\int_0^\infty \frac{\sin x}{x}\, dx
  1. Mauris 3^{n+1} ac sqrt(17) orci x=yz eget x+1 id.
\begin{bmatrix} 0&1\\ -1&0 \end{bmatrix}
  1. Vivamus sed p_3 nisl x/y=z eget x^{10} at r+s lorem.
\sum_{k=1}^\infty \frac{(-1)^k}{k}
  1. Nam ut \ln x libero a/b sed t_1 quis x^5 erat.
\int_0^1 (x^3+x^2)\, dx
  1. Maecenas non q/p lacus sqrt(19) eget |x+1| vel n-1 .
\nabla\times \mathbf{F}
  1. Duis eget x^{1/2} velit a=b sit w_n amet x^n z^3 .
\int \frac{1}{x^2+1}\, dx
  1. Vestibulum f'(x) ante y=x eget 1/(x^2) id 3x nec sqrt(23) .
\sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}
  1. Cras ac r_2 magna x=y non s^2 eget x^{-3} 1/(1+x) .
\begin{bmatrix} 1&3&5\\ 2&4&6 \end{bmatrix}
  1. Etiam nec p_7 orci x*y ac u_1 vitae dui sqrt(29) .
\frac{d}{dx}(\sin x)=\cos x
  1. Donec ut x^8 mauris a=b+c eget 2t+7 id s_n ligula.
\int_0^\pi \sin x\, dx
  1. Nulla a 2^k mauris 1/(x+2) eget u'=ku et v+w nisl.
\prod_{n=1}^N n
  1. Nam nec x_{ij} nisl x=y et x! at t^3+1 risus sqrt(31) .
\int (3x^2-2x)\, dx
  1. Sed eget m(x) nibh x/(y+1) sed p/q eget e^t sit.
\sum_{n=0}^\infty \frac{x^n}{n!}
  1. Aliquam r_8 elit x^2-5 eu sqrt(37) ut uvw felis.
\det\begin{bmatrix} 3&1&4\\ 1&5&9\\ 2&6&5 \end{bmatrix}
  1. Integer n^n urna x*y/z vel u^{-1} nec 3x+4 lorem.
\int_0^1 \ln x\, dx
  1. Mauris t_n lorem x^(-1) id x^3-1 at \sqrt{x} sed.
y'+p(x)y=q(x)
  1. Cras ac w(t) leo x+y=z eget p^2 non r^4 a=b .
\oint_C \mathbf{E}\cdot d\mathbf{l}
  1. Suspendisse x_8 orci x=y/z id 1/(2x) consectetur a^k sqrt(41) .
\int (x^4-x)\, dx
  1. Aenean sit x^{11} amet a*(b+c) nunc 2^p nec z(w) .
\begin{bmatrix} 4&1\\ 2&-3 \end{bmatrix}
  1. Ut id x/y risus sqrt(43) eget x+3 non \phi^2 ligula.
\sum_{n=1}^\infty \frac{1}{n}
  1. Nam vitae t^5 ipsum a=b sed q(x) eget r(x) dui.
\int_0^1 x^x\, dx
  1. Phasellus x_{10} nec x-y+z arcu e^{i\theta} non f_0 sqrt(47) .
\frac{d}{dt}\begin{bmatrix}x\\y\end{bmatrix}
  1. Curabitur x_1 id x/(1+y) urna \alpha^2 eget \beta^3 x+y=z .
\int_0^2 x^3\, dx
  1. Duis pulvinar \theta metus sqrt(5) id x^2-4 nec 3x a/b .
x^3-4x
  1. Integer sed \gamma diam x+1 eget x^4 eget \delta m/n .
\sqrt{x^2+1}
  1. Nulla eget \lambda felis x/(x-1) quis x^7 non \mu elit.
\int_1^2 x^2\, dx
  1. Sed eu \sigma ante a=b non 1/(x+2) et x^9 pharetra.
e^{x^2}
  1. Donec quis \rho risus y=x^2 ut \eta sed x^{11} x/y .
\log(1+x)
  1. Aliquam sit \tau amet a/b-c/d purus x^{-4} eget w .
\sin(x^2)
  1. Vivamus vel \phi ipsum x*y sed x^2-y^2 non r^5 .
\cosh x
  1. Donec eget \psi metus x=y+z id x_3 sed x_4 felis.
\sinh x
  1. Aenean rutrum p_7 nisl x/y eget q_7 ut r_7 elit.
\tan x
  1. Curabitur vel t_9 lorem x^3 ac x+4 sed x^6 .
\cot x
  1. Nulla vitae p_{10} nisl a=b nec x/(2-y) et x-3 .
\sec x
  1. Phasellus a q_{10} dui x/y eget r_{10} non s_{10} .
\csc x
  1. Sed \alpha_1 arcu x+y ac \beta_1 non \gamma_1 urna.
x^x
  1. Donec eget \delta_1 justo m/n vel \epsilon_1 nec \zeta_1 .
\sqrt[3]{x}
  1. Ut nec \eta_1 lorem sqrt(11) eget \theta_1 non \iota_1 .
\frac{1}{x}
  1. Aenean vel \kappa_1 erat x/z non \lambda_1 ut \mu_1 .
x^n
  1. Cras ac \nu_1 turpis x/(x+3) nec \xi_1 at o_1 .
\sum_{k=0}^\infty x^k
  1. Pellentesque p_1 velit a/b+c a q_1 non r_1 lacus.
\int_0^1 x^4\, dx
  1. Mauris id s_1 lacus sqrt(13) et t_1 eget u_1 .
\int_0^\pi x\sin x\, dx
  1. Vivamus non v_1 elit x*y sed w_1 eget z_1 .
\int_0^\infty e^{-x}\, dx
  1. Sed a_2 arcu x-y non b_2 vel c_2 dapibus.
\frac{d}{dx}x^n
  1. In hac d_2 habitasse x=y eget e_2 et f_2 .
\frac{d}{dx}\ln x
  1. Donec non g_2 ipsum a/b eget h_2 non i_2 felis.
\frac{d}{dx}\sin x
  1. Mauris a j_2 sem x/y vel k_2 eget l_2 arcu.
\frac{d}{dx}\cos x
  1. Pellentesque m_2 velit sqrt(19) at n_2 eget o_2 .
\frac{d}{dx}\tan x
  1. Suspendisse at p_2 dui x+z ac q_2 sed r_2 ante.
\frac{d}{dx}\cot x
  1. Donec ut s_2 velit sqrt(23) et t_2 id u_2 .
\frac{d}{dx}\sec x
  1. Quisque nec v_2 nisi x^2/(1+x) sed w_2 ac z_2 .
\frac{d}{dx}\csc x
  1. Nam et a_3 tortor x/(y-z) ac b_3 sed c_3 ligula.
e^x
  1. Morbi sed d_3 tortor x*y id e_3 vel f_3 arcu.
e^{x^2}
  1. In eget g_3 dui x=(y+z) et h_3 eget i_3 lacus.
\ln(1+x)
  1. Donec j_3 libero sqrt(7) non k_3 id l_3 arcu.
\log_{10} x
  1. Aliquam m_3 nulla a=b at n_3 et o_3 tortor.
\arcsin x
  1. Curabitur p_3 metus x^2-y^2 eget q_3 et r_3 leo.
\arccos x
  1. Maecenas s_3 erat x/y nec t_3 at u_3 tortor.
\arctan x
  1. Ut id v_3 ante sqrt(5) vel w_3 nec z_3 risus.
\sinh x
  1. Pellentesque a_4 felis x^2/z nec b_4 vel c_4 nunc.
\cosh x
  1. Cras eget d_4 arcu x^n at e_4 quis f_4 sem.
\tanh x
  1. Fusce vel g_4 leo a=b nec h_4 sed i_4 lectus.
\coth x
  1. Etiam ut j_4 arcu sqrt(47) id k_4 nec l_4 sapien.
\frac{1}{1+x}
  1. Sed sit m_4 amet x/(y+z) mauris n_4 eget o_4 .
\frac{1}{1+x^2}
  1. Curabitur p_4 arcu m/n at q_4 ac r_4 est.
\frac{1}{\sqrt{x}}
  1. Donec vel s_4 erat x^3 eget t_4 sed u_4 eros.
\sqrt{x}
  1. Vestibulum v_4 urna x=y vel w_4 nec z_4 urna.
\sqrt[4]{x}
  1. Suspendisse a_5 justo sqrt(11) eget b_5 nec c_5 arcu.
x\ln x
  1. Nam vitae d_5 elit a=b ac e_5 et f_5 felis.
\ln(x^2+1)
  1. Cras vel g_5 ante x/y sed h_5 non i_5 ipsum.
\ln(x^3-1)
  1. Nullam j_5 lorem x^z eget k_5 a l_5 pharetra.
x^x
  1. Sed m_5 arcu a/b id n_5 non o_5 felis.
\sqrt{x+1}
  1. Donec vel p_5 risus x+y=z eget q_5 vel r_5 nisl.
\sqrt{x^2+x+1}
3
  1. Lorem ipsum x^2 + \alpha dolor a/b sit amet \beta + \gamma consectetur x+y=z adipiscing \sqrt{1+x^2} elit.
\begin{aligned} I_1 &= \int_0^\infty x^3 e^{-x^2}\, dx \\ &= \frac{1}{2} \Gamma\!\left( \frac{4}{2} \right) \end{aligned}
  1. Sed et \theta/3 ante sqrt(5)/2 eget \pi^2 augue \sigma+\mu sit amet x/(y+1) sem.
\begin{aligned} A &= \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 1 & 5 & 6 \\ 0 & 0 & 1 & 7 \\ 0 & 0 & 0 & 1 \end{bmatrix} \\ A^{-1} &= \begin{bmatrix} 1 & -2 & -? & \ldots \\ 0 & 1 & -5 & \ldots \\ 0 & 0 & 1 & -7 \\ 0 & 0 & 0 & 1 \end{bmatrix} \end{aligned}
  1. Curabitur posuere \delta x + \phi odio x^2+y^2=1 a \eta mi \lambda^3 nec a=b mauris.
\begin{aligned} \nabla\cdot\mathbf{F} &= \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y} + \frac{\partial R}{\partial z} \\ \text{where } \mathbf{F} &= \langle P,Q,R\rangle \end{aligned}
  1. In eu \int_0^1 t^n dt nunc sqrt(2)/2 nec x_0 arcu \psi + \omega porta x*y .
\begin{aligned} S &= \sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)^3} \\ &= \frac{\pi^3}{32} \end{aligned}
  1. Praesent elementum \nabla\times\mathbf{F} velit a/(b+c) nec u+3v vitae w^5 et x/y nunc.
\begin{aligned} \oint_C \mathbf{F}\cdot d\mathbf{r} &= \iint_S (\nabla\times\mathbf{F})\cdot \mathbf{n}\, dS \\ \text{(Stokes Thm.)} \end{aligned}
  1. Integer blandit \sqrt{x+\sqrt{x+\sqrt{x}}} ante (a+b)/c nec \alpha\beta\gamma id \rho^4 erat x=y .
\begin{aligned} f(x) &= \sqrt{1 + \sqrt{2 + \sqrt{3 + x}}} \\ f'(x) &= \frac{1}{2f(x)\sqrt{3+x}} \end{aligned}
  1. Vivamus mattis \xi + 2\eta erat tan(pi/8) eget x_1+x_2+x_3 eget \beta^2 a*b .
\begin{aligned} \int_0^\pi \sin^3(x)\, dx &= \int_0^\pi (1-\cos^2 x)\sin x\, dx \\ &= 2 \end{aligned}
  1. Sed at \Gamma(n) felis sum(i^2) vitae \zeta(3) nec x^7 interdum x/(y-z) .
\begin{aligned} \Gamma(z) &= \int_0^\infty t^{z-1} e^{-t}\, dt \\ \Gamma\!\left(\tfrac12\right) &= \sqrt{\pi} \end{aligned}
  1. Morbi euismod x_5 lectus sqrt(11) ac \lambda + \tan x non \theta_n at x+1 arcu.
\begin{aligned} \frac{d}{dx}\left( x^2 e^{\sin x} \right) &= 2x e^{\sin x} + x^2 e^{\sin x}\cos x \end{aligned}
  1. Donec a \cos(x^2) nibh x*y/z sed \sin(x^3) at \tanh(x^4) pellentesque x/(1+y) .
\begin{aligned} E &= \begin{bmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 3 & 5 & 7 & 11 \\ 1 & 4 & 6 & 8 & 12 \\ 0 & 1 & 0 & 2 & 1 \\ 3 & 1 & 4 & 1 & 5 \end{bmatrix} \end{aligned}
  1. Cras id \phi\psi ligula sqrt(13) sit \Omega(k) amet x^{-3} nec a+b rutrum.
\begin{aligned} \iint_D (x+y)\, dA &= \int_0^1\int_0^{1-x} (x+y)\, dy\, dx \end{aligned}
  1. Duis porta \sqrt{x^4+4x^2+1} velit x=y in n! at \chi^2 euismod sum_{i=1}^n i .
\begin{aligned} \int \frac{1}{x^4+1}\, dx &= \frac12 \arctan x - \frac14\ln(x^2- \sqrt2 x+1) \end{aligned}
  1. Proin suscipit \int_0^1 x^x dx ante x/(x-1) vel e^{x^3} tempus y^2=x^3 vitae nisl.
\begin{aligned} x^x &= e^{x\ln x} \\ \frac{d}{dx}(x^x) &= x^x(\ln x + 1) \end{aligned}
  1. Vestibulum pharetra \int e^{x^2}\,dx ex sqrt(17) ut \tan^{-1}(x) eget x+y eget felis.
\begin{aligned} \int e^{x^2}\, dx &= \text{(nonelementary)} \\ \text{erfi}(x) &= -i\, \text{erf}(ix) \end{aligned}
  1. Suspendisse sit amet \sin(xy) nisl x^5 eget \cos(x/y) eget x/(z+w) lorem.
\begin{aligned} \int_0^\pi \cos(nx)\cos(mx)\, dx &= \begin{cases} 0, & m\neq n \\ \pi/2, & m=n\neq 0 \end{cases} \end{aligned}
  1. Curabitur gravida \sqrt{x+\sqrt{2+\sqrt{3+x}}} magna x*y eget x_8 nec a-b purus.
\begin{aligned} B &= \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 5 & 7 & 9 \\ 1 & 0 & 2 & 3 \\ 4 & 4 & 1 & 0 \end{bmatrix} \\ \text{rank}(B) &= 4 \end{aligned}
  1. Vivamus luctus \nabla^2 f augue m/n eget \Delta u et \partial_x f vehicula x^2-1 .
\begin{aligned} \nabla^2 f &= \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} \end{aligned}
  1. Maecenas mattis \zeta(s) nulla x/(y+z) eget \eta(s) quis \Gamma(s) posuere a*b .
\begin{aligned} \zeta(s) &= \sum_{n=1}^\infty \frac{1}{n^s},\quad \Re(s)>1 \\ \Gamma(s)\zeta(s) &= \int_0^\infty \frac{t^{s-1}}{e^t-1}\, dt \end{aligned}
  1. Sed non \int_0^\infty x^n e^{-x}\, dx orci x*y vitae \cos(\sqrt{x}) at sqrt(29) velit.
\Gamma(n+1)=n!
  1. Pellentesque pharetra \sqrt[3]{x^2+\sqrt{x}} risus x+y=z sit \alpha^3 amet x/(y-x) elit.
\begin{aligned} \int \frac{x^2+1}{x^4+1}\, dx &= \frac12\arctan x + \frac14\ln(x^2-\sqrt2 x+1) \end{aligned}
  1. Integer ornare \sin(x^3) libero x/y quis \tan(\sqrt{x}) sed \sec(x^2) x/(2+y) .
\begin{aligned} \int x^2 \sin(x^3)\, dx &= -\frac13 \cos(x^3) \end{aligned}
  1. Donec bibendum \nabla\cdot(x\mathbf{i}+y\mathbf{j}) tortor a-b vitae x_9 euismod x+z .
\nabla\cdot\langle x,y\rangle = 2
  1. Aenean luctus \frac{d}{dx}(x^x) est x^3 eget \log(x^2+1) mauris x/(x+3) .
x^x(\ln x + 1)
  1. Sed vehicula \sqrt{x^2+y^2+z^2} purus a/(b+c) eget \arctan(y/x) sit x*y amet arcu.
\begin{aligned} r &= \sqrt{x^2+y^2+z^2} \\ \theta &= \arctan(y/x) \end{aligned}
  1. Cras feugiat \int_0^1 t^t dt ex x^2/(1+x) non \sin(x^2) eget x/z velit.
\int_0^1 t^t dt = 0.78343\ldots
  1. Integer dapibus \cos(x^5) diam x-y nec \tan(x^4) non x/y+z felis.
\begin{aligned} \int \cos(x^5) x^4\, dx &= \sin(x^5) \end{aligned}
  1. Aliquam sit \sqrt{x+\sqrt{x+\sqrt{x}}} amet x/(y+1) tellus \psi^3 eget a*b arcu.
\begin{aligned} M &= \begin{bmatrix} 2&1&0&0\\ 1&2&1&0\\ 0&1&2&1\\ 0&0&1&2 \end{bmatrix} \\ \lambda_k &= 2+2\cos\left(\frac{k\pi}{5}\right) \end{aligned}
  1. Phasellus lacinia \log(\log x) felis sqrt(31) eget \exp(\sqrt{x}) in x/y lacus.
\int \frac{1}{x\ln x}\, dx = \ln(\ln x)
  1. Vestibulum ac \sin(\ln x) lorem x/(x^2+1) sed \cos(\ln x) nec x+1 massa.
\frac{d}{dx}\sin(\ln x)=\frac{\cos(\ln x)}{x}
  1. Donec suscipit \int x\cos x\, dx diam x^2 eget x\sin x malesuada a=b .
x\sin x + \cos x + C
  1. Duis accumsan \theta^4 est x*y a \beta^3 id \gamma^2 posuere a/(b-c) .
\begin{aligned} \int_0^\infty e^{-ax^2}\, dx &= \frac12\sqrt{\frac{\pi}{a}} \end{aligned}
  1. Etiam aliquet \nabla\times\mathbf{F} felis x=y at \nabla\cdot\mathbf{G} odio x+z purus.
\nabla\times\langle yz,xz,xy\rangle
  1. Curabitur sed \log(x!) urna x/(x-2) varius \Gamma(x+1) eget a+b nisi.
\Gamma(n+1)=n!
  1. Pellentesque non x^{x^2} quam sqrt(2) sed x\log x vel x/(x+1) sapien.
\frac{d}{dx}(x^{x^2}) = x^{x^2}(2x\ln x + x)
  1. Aenean dictum \cosh(x^2) nibh x^(1/3) eget \sinh(x^2) x/(y+5) orci.
\frac{d}{dx}\cosh(x^2)=2x\sinh(x^2)
  1. Duis vitae \tan^{-1}(\sqrt{x}) lorem x=y nec \cot(\sqrt{x}) id a/b+c mi.
\frac{d}{dx}\tan^{-1}(\sqrt{x}) = \frac{1}{2\sqrt{x}(1+x)}
  1. Maecenas varius \sin(x^3+x) dui x/(y+z) eget \cos(x^3+x) sit m/n amet arcu.
\int x^2\cos(x^3)\, dx = \frac13\sin(x^3)
  1. Nunc convallis \exp(\sin(\ln x)) metus x+y=z eget \ln(1+\sin x) x/(x+e) arcu.
\frac{d}{dx}\exp(\sin(\ln x))
  1. Sed mattis \tanh(x^2) nibh x*y eget \coth(x^2) vestibulum x^3 sem.
\begin{aligned} \frac{d}{dx}\tanh(x^2) &= 2x\operatorname{sech}^2(x^2) \end{aligned}
  1. Donec at \sqrt{e^{x^2}+1} dui a=b ac \tan(\sqrt{x}+\sqrt{y}) eu sqrt(37) elit.
\sqrt{e^{x^2}+1}
  1. Curabitur suscipit \sin(\sqrt{x+1}) tortor x/z vitae \cos(\sqrt{x+1}) x-1 .
\frac{d}{dx}\sin(\sqrt{x+1})
  1. Quisque interdum \log(\sqrt{x^2+1}) leo a/b vel \sqrt{x^2+y^2} id x=y nisl.
\ln(\sqrt{x^2+1})
  1. Vestibulum ac \sqrt[4]{x^3+y^3} elit x*y/z et \sqrt[3]{x^2} nec x/(x^2+3) felis.
\sqrt[4]{x^3+y^3}
  1. Fusce pretium \ln(\ln(\ln x)) sapien sqrt(11) quis \operatorname{Li}_2(x) non x+y dolor.
\begin{aligned} \operatorname{Li}_2(x) &= -\int_0^x \frac{\ln(1-t)}{t}\, dt \end{aligned}
  1. Donec porta \int_0^\infty \cos xt/(1+t^2)\, dt erat x-z non \int_0^1 t^t dt at x/y felis.
\frac{\pi}{2} e^{-|x|}
  1. Aliquam sagittis \frac{d}{dx}\log(\Gamma(x)) ex a/(b+c) nec \psi(x) sed x^2 felis.
\psi(x) = \frac{\Gamma'(x)}{\Gamma(x)}
  1. Ut luctus \frac{1}{\sqrt{x}} lorem x-y non \frac{1}{x^{3/2}} vehicula m/n .
\int x^{-3/2}\, dx = -2x^{-1/2}
  1. Mauris elementum \sqrt{x+\sqrt{x+\sqrt{x}}} nisl x*y/(z+w) ut \alpha^7 eget sqrt(13) arcu.
\sqrt{x+\sqrt{x+\sqrt{x}}}
  1. Etiam luctus \sin(\ln(\ln x)) sapien x/(x+4) eget \cos(\ln(\ln x)) nec a*b odio.
\frac{d}{dx}\sin(\ln(\ln x))
  1. Phasellus lorem \sqrt{1+x^4} purus sqrt(17) non \sqrt{1+x^8} eget x/y metus.
\sqrt{1+x^4}
4
  1. Nulla sit amet \alpha^4+\beta^4 velit x*y/(z+w) eu \sqrt[3]{1+x^3} sed \log(\log x) eget a/b nisl.
\begin{aligned} I_{51} &= \int_0^1 \frac{\ln(1+x)}{1+x^2}\, dx \\ &= \sum_{n=1}^\infty (-1)^{n+1} \frac{1}{n} \int_0^1 x^n\, dx \\ &= \sum_{n=1}^\infty (-1)^{n+1} \frac{1}{n(n+1)} \end{aligned}
  1. Donec accumsan \nabla f = \langle f_x,f_y\rangle sapien x/(x-2) quis \Delta u a \Gamma(s) a+b .
\begin{aligned} \nabla^2 u &= \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \\ \text{Solve } &\; \nabla^2 u = -1,\; u|_{\partial D}=0 \end{aligned}
  1. Vestibulum nec \sqrt{1+\sqrt{1+\sqrt{1+x}}} lacus x+y=z vel \sin(\sqrt{x}) sed sqrt(5) vehicula.
\begin{aligned} M_{53} &= \begin{bmatrix} 1 & 2 & 3 & 4 & 5 \\ 0 & 1 & 2 & 3 & 4 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix} \\ \det(M_{53}) &= 1 \end{aligned}
  1. Aliquam mattis \int_0^\infty x^{s-1}e^{-x} dx erat a/(b+c) sit \zeta(2) amet m/n lacus.
\begin{aligned} \zeta(2) &= \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6} \\ \zeta(4) &= \frac{\pi^4}{90} \end{aligned}
  1. Curabitur convallis \sin(x^3+x) nisl x*y/z eu \cos(x^3+x) et \tan(\ln x) a+b .
\begin{aligned} \int \sin(x^3+x)\, dx &= \int \sin(x)(e^{i x^3}+e^{-i x^3})/2\, dx \\ \text{(nonelementary)} \end{aligned}
  1. Maecenas commodo \log(\sqrt{x^2+4x+5}) velit x/(y+1) sit \sqrt{x^2+y^2} amet sqrt(11) nunc.
\begin{aligned} \sqrt{x^2+4x+5} &= \sqrt{(x+2)^2+1} \\ \int \log(\sqrt{x^2+4x+5})\, dx &= x\log\left(\sqrt{(x+2)^2+1}\right) - 2\sinh^{-1}(x+2) \end{aligned}
  1. Duis tincidunt \tanh(x^2+y^2) felis x/(x+3) ac \coth(xy) sed a/(b-c) turpis.
\begin{aligned} \nabla\cdot\langle \tanh(x^2+y^2), xy, x-y\rangle &= 2x\,\operatorname{sech}^2(x^2+y^2) + x-y + y \end{aligned}
  1. Suspendisse pharetra \operatorname{Li}_2(x) magna sqrt(7) vel \operatorname{Li}_3(x) vitae x*y mi.
\begin{aligned} \operatorname{Li}_2(x) &= -\int_0^x \frac{\ln(1-t)}{t}\, dt \\ \operatorname{Li}_3(x) &= \int_0^x \frac{\operatorname{Li}_2(t)}{t}\, dt \end{aligned}
  1. Etiam non \sqrt[4]{x^3+y^3+z^3} arcu x/(z+w) a \sqrt[5]{x+y+z} id m/n lacus.
\begin{aligned} R_4 &= \sqrt[4]{x^3+y^3+z^3} \\ R_5 &= \sqrt[5]{x+y+z} \end{aligned}
  1. Integer vitae \cos(\sqrt{x+1}) felis x+y=z nec \sin(\sqrt{x+2}) id a*b risus.
\begin{aligned} \frac{d}{dx}\cos(\sqrt{x+1}) &= -\frac{1}{2\sqrt{x+1}}\sin(\sqrt{x+1}) \end{aligned}
  1. In pretium \sqrt{x+\sqrt{2+\sqrt{3+\sqrt{x}}}} lorem x*(y+z) sed \ln(\ln(\ln x)) nisi x/y .
\begin{aligned} f(x) &= \sqrt{x+\sqrt{2+\sqrt{3+\sqrt{x}}}} \\ f'(x) &= \frac{1}{2f(x)} \left( 1 + \frac{1}{2\sqrt{3+\sqrt{x}}} \frac{1}{2\sqrt{x}} \right) \end{aligned}
  1. Praesent dictum \nabla^2(\sin(xy)) augue x/(y-x) eget \partial_x\partial_y f ac sqrt(13) felis.
\begin{aligned} \nabla^2(\sin(xy)) &= \frac{\partial^2}{\partial x^2}\sin(xy) + \frac{\partial^2}{\partial y^2}\sin(xy) \\ &= -y^2\sin(xy) - x^2\sin(xy) \\ &= -(x^2+y^2)\sin(xy) \end{aligned}
5

Oh, one last thing - my favorite formula is:

\frac{1}{\sqrt{2\pi}\sigma}\int_{-\infty}^{\infty} e^{-(x-\mu)^2/(2\sigma^2)} \, dx = 1!